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Toggle## Class 7, Maths, Chapter 12, Exercise 12.1 Solutions

**Q.1. Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.**

**(i) Subtraction of z from y.**

**(ii) One-half of the sum of numbers x and y.**

**(iii) The number z multiplied by itself.**

**(iv) One-fourth of the product of numbers p and q.**

**(v) Numbers x and y both squared and added.**

**(vi) Number 5 added to three times the product of numbers m and n.**

**(vii) Product of numbers y and z subtracted from 10.**

**(viii) Sum of numbers a and b subtracted from their product.**

**Ans:**

(i) Subtraction of z from y.

= Y – z

(ii) One-half of the sum of numbers x and y.

$=\frac{x+y}{2}$

(iii) The number z multiplied by itself.

=z × z = z^{2}

(iv) One-fourth of the product of numbers p and q.

$\mathsf{=}\frac{\mathsf{1}}{\mathsf{4}}\mathsf{(p\times q)=}\frac{\mathsf{pq}}{\mathsf{4}}$

(v) Numbers x and y both squared and added.

= x^{2} + y^{2}

(vi) Number 5 added to three times the product of numbers m and n.

= 3mn + 5

(vii) Product of numbers y and z subtracted from 10.

= 10 – (y x z) = 10 – yz

(viii) Sum of numbers a and b subtracted from their product.

= (a x b) – (a + b) = ab- (a + b)

**Q.2. (i) Identify the terms and their factors in the following expressions Show the terms and factors by tree diagrams.**

**(a) x – 3 **

**(b) 1 + x + x ^{2} **

**(c) y – y ^{3}**

**(d) 5xy ^{2} + 7x^{2}y **

**(e) – ab + 2b ^{2} – 3a^{2}**

**(ii) Identify terms and factors in the expressions given below:**

**(a) – 4x + 5 **

**(b) – 4x + 5y **

**(c) 5y + 3y ^{2}**

**(d) xy + 2x ^{2}y^{2} **

**(e) pq + q **

**(f) 1.2 ab – 2.4 b + 3.6 a**

**(g) **** $\frac{\mathsf{3}}{\mathsf{4}}\mathsf{x+}\frac{\mathsf{1}}{\mathsf{4}}$**

**(h) 0.1p ^{2} + 0.2q^{2}**

**(ii)**

**Q.3. Identify the numerical coefficients of terms (other than constants) in the following expressions:**

**(i) 5 – 3t ^{2} **

**(ii) 1 + t + t ^{2} + t^{3} **

**(iii) x + 2xy + 3y**

**(iv) 100m + 1000n **

**(v) – p ^{2}q^{2} + 7pq **

**(vi) 1.2 a + 0.8 b**

**(vii) 3.14 r ^{2} **

**(viii) 2 (l + b)**

**(ix) 0.1 y + 0.01 y ^{2}**

**Ans:**

**Q.4. (a) Identify terms which contain x and give the coefficient of x.**

**(i) y ^{2}x + y **

**(ii) 13y ^{2} – 8yx **

**(iii) x + y + 2**

**(iv) 5 + z + zx **

**(v) 1 + x + xy **

**(vi) 12xy ^{2} + 25**

**(vii) 7x + xy ^{2}**

**(b) Identify terms which contain y ^{2} and give the coefficient of y^{2}.**

**(i) 8 – xy ^{2} **

**(ii) 5y ^{2} + 7x **

**(iii) 2x ^{2}y – 15xy^{2} + 7y^{2}**

**Ans:**

**(a)**

**(b)**

**Q.5. Classify into monomials, binomials and trinomials.**

**(i) 4y – 7z **

**(ii) y ^{2} **

**(iii) x + y – xy **

**(iv) 100**

**(v) ab – a – b **

**(vi) 5 – 3t **

**(vii) 4p ^{2}q – 4pq^{2} **

**(viii) 7mn**

**(ix) z ^{2} – 3z + 8 **

**(x) a ^{2} + b^{2} **

**(xi) z ^{2} + z**

**(xii) 1 + x + x ^{2}**

**Ans:**

**Monomials:** An expression with **only one term** is called a **monomial**.

**Binomials:** An expression with **only two term** is called a **binomial.**

**Trinomials:** An expression with **only three term** is called **a trinomial**.

**Q.6. State whether ****a given pair of terms is of like or unlike terms.**

**(i) 1, 100 **

**(ii) **** $-7x,\frac{5}{2}x$**

**(iii) –29x,–29y**

**(iv) 14xy, 42yx **

**(v) 4m ^{2}p, 4mp^{2} **

**(vi) 12xz, 12x ^{2}z^{2}**

**Ans:**

**Like terms**: When term have the same algebraic factors, they are like terms.

All constant are like terms.

**Unlike terms: **The terms have different algebraic factors, they are unlike terms.

**Q.7. Identify like terms in the following:**

**(a) – xy ^{2}, – 4yx^{2}, 8x^{2}, 2xy^{2}, 7y, – 11x^{2}, – 100x, – 11yx, 20x^{2}y, – 6x^{2}, y, 2xy, 3x**

**(b) 10pq, 7p, 8q, – p ^{2}q^{2}, – 7qp, – 100q, – 23, 12q^{2}p^{2}, – 5p^{2}, 41, 2405p, 78qp, 13p^{2}q, qp^{2}, 701p^{2}**

**Ans:**

**(a) Like terms:** When term have the same algebraic factors, they are like terms.

(i) -xy^{2}, 2xy^{2}

(ii) -4yx^{2}, 20x^{2}y

(iii) 8x^{2},-11x^{2}, -6x^{2}

(iv) 7y, y

(v) -100x, 3x

(vi) -11yx, 2xy

(b) **Like terms:** When term have the same algebraic factors, they are like terms.

(i) 10 pq, -7pq,78qp

(ii) 7p, 2405p

(iii) 8q,-100q

(iv) -p^{2}q^{2},12q^{2} p^{2}

(v) -23,41

(vi) -5p^{2},701p^{2}

(vii) 13p^{2}q, qp^{2}

## NCERT Solutions For Class 7 Maths, Chapter 12 Algebraic Expressions (All Exercises)

**Class 7, Maths, Chapter 12, Algebraic Expressions **

**Class 7, Maths, Chapter 12, Algebraic Expressions, Exercise 12.1** **← You are here**

**Class 7, Maths, Chapter 12, Algebraic Expressions, Exercise 12.2**

**Class 7, Maths, Chapter 12, Algebraic Expressions, Exercise 12.3**

**Class 7, Maths, Chapter 12, Algebraic Expressions, Exercise 12.4**